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Applications of Sampling and Quantization

 

Q1.  An analog FM radio transmitter broadcasts between approximately 88 and 108 MHz. If the entire received band (i.e., all radio programmes in the FM band) would need to be stored in digital format, what is then the required sampling rate?        

 

Q2. A single FM programme has a typical frequency sweep of 200 kHz. For example, Radio Bob&Luk broadcasts between 106.02 MHz and 106.22 MHz on Mondays 13:00-15:00 and Tuesdays 11:00-12:00 (i.e., 1.8% of the time each week).

(a) What bandwidth is needed to digitize this station without loss of quality?        

(b) For high-fidelity recording of this channel (e.g., on DVD, in-flight entertainment systems, etc.), a signal-to-quantization-noise ratio (SQNR) of 74 dB (decibel) is aimed for. Given that SQNR for a uniform quantizer is approximately

SQNR = (1.76 + 6.02 b) dB

for b-bit encoding, determine the value of b.            

(c) In practice, 16-bit encoding is used instead.

(i) Determine the SQNR corresponding to such 16-bit encoding.            

(ii) Give one possible reason for the difference between b=16 and the value of b that you obtained in part (b).     

(iii) What dynamic range of the sound is thus achieved?              

 

Q3. Companders (a contraction of compress and expand) are used in voice communications to improve the signal-to-noise ratio (SNR). They exploit the logarithmic characteristic of human hearing for the perception of sound. Different compander ‘laws’ are in used in different countries and for different applications. For example, in UNIX, Java, etc., the m-255 compander characteristic

enables a SNR of 77 dB to be achieved. This SNR should be compared to uncompressed (linear) quantization, which achieves only 44 dB using the same number of bits to quantize the sound level.

(a) Given that one extra bit is needed for the positive/negative sign (polarity) of a signal, determine the number of amplitude levels of the digitized signal.              

(b) If this signal is sampled at 8 kHz, determine the bit rate needed to store 3 seconds of this digitized (i.e., sampled and quantized) audio signal.        

Q4. Digitized speech for voice over a public telephone network uses DECT (Digital Enhanced Cordless Telecommunications) technology. One requires a minimum SNR of 25 dB, plus a further 30 dB for a good dynamic range. How many bits are needed for the encoding?